One becomes two

One becomes two. The life of one cell, drawn as a statechart. Each glass slide is a state a cell can be in. Each thread is a step it can take. TLC, a model checker, tried every one: 61 states and 77 steps. A gold thread is a healthy cell, a red thread is what TLC found when a check breaks, and a pale thread is every other step. Below, a tissue of pink cells like a stained slide; one cell, outlined in gold, is where the thread begins.
  • Charted with the /statechart skill by @poteto.
  • Modelled in TLA+, checked by TLC and laid out by pele.
  • Drawn in JavaScript with simulated pencil, pastel and gel pen.
  • Lettering in Kevin Sans, traced from A. V. Hershey’s 1967 fonts.
  • The code and drawings are on GitHub, under the MIT license.
Getting ready (interphase). A large cell with its nucleus, mitochondria and folds of membrane; sugar molecules drift toward it. On brown paper, a long DNA double helix. On the left, rays of sunlight break it; on the right, the protein p53 clamps onto it and holds the cell still. On dark teal, the DNA unzips at a fork and each half becomes a new double helix, gold and pale blue. On graph paper, two columns of coloured beads match one for one with a red tick, and a cell sketch now holds two of every chromosome. On plum paper, a broken DNA helix with two ring-shaped repair proteins stitching the ends together. A cell breaks into neat round pieces, and a larger cleaner cell swallows them. Dividing (mitosis). On black, a tangle of coloured DNA threads on the left; on the right, the threads have coiled into X-shaped, banded chromosomes. On navy, two golden spindle poles shine fibres in from the left and right while pieces of the broken nucleus drift between them. Gold fibres catch chromosomes. On the left, one is held from both sides; on the right, one is held from one side only, its loose side glowing red. On pink paper, six purple chromosomes line up in a column in the middle, with fibres running to a pole on each side. On terracotta, V-shaped chromatids are pulled to the far left and far right poles. On peach paper, a long cell with a pinched waist, a new nucleus forming at each end. Two daughter cells, each with its own nucleus and mitochondria, still joined by a thin bridge tied with a red ring. Three pairs of daughter cells. Left: one has an extra chromosome and one is short. Middle: each has one of everything. Right: both carry a red mark, the copied damage. Each daughter begins again at the top. What TLC checked, beside a ring showing one cycle: G1, S, G2 and M.

Read the chart as text

A statechart of the cell cycle, modelled in TLA+ and checked by TLC, which reached 61 states and 77 steps. Each state below lists the steps that leave it.

Getting ready (interphase)

Growing (G1)
the DNA is damaged [p53 broken] → Damaged, and p53 is broken
no signal to grow → Resting (G0)
passes the first check → Copying its DNA (S)
the DNA is damaged → Damaged, held by p53
Damaged, and p53 is broken
the damage is repaired → Growing (G1)
copies it anyway → Copying damaged DNA
Resting (G0)
a growth signal arrives → Growing (G1)
Copying its DNA (S)
the copy is done → Checking the copy (G2)
Damaged, held by p53
the damage is repaired → Growing (G1)
too much damage → Dies on purpose (apoptosis)
Copying damaged DNA (breaks a rule)
the damage is copied as a mutation → Checking the copy (G2)
Checking the copy (G2)
the DNA is damaged → Damaged, held at the second check
passes the second check → Coiling up (prophase)
Damaged, held at the second check
the damage is repaired → Checking the copy (G2)
too much damage [p53 working] → Dies on purpose (apoptosis)

Endings

Dies on purpose (apoptosis)
the end
Two cells with the wrong chromosomes (breaks a rule)
the end
Two healthy cells
the end
Two cells carrying a mutation (breaks a rule)
the end

Dividing (mitosis)

Coiling up (prophase)
the nucleus opens → The spindle reaches in (prometaphase)
The spindle reaches in (prometaphase)
fibres catch some chromosomes → Some caught, the check waits
fibres catch some [check broken] → Some caught, the check is broken
Some caught, the check waits
every chromosome is caught → Lined up in the middle (metaphase)
Some caught, the check is broken
every chromosome is caught → Lined up in the middle (metaphase)
pulled apart anyway → Pulled apart too soon
Lined up in the middle (metaphase)
the sisters are pulled apart → Sisters pulled apart (anaphase)
Pulled apart too soon (breaks a rule)
two nuclei form → Two nuclei form (telophase)
Sisters pulled apart (anaphase)
two nuclei form → Two nuclei form (telophase)
Two nuclei form (telophase)
the cell pinches → Pinching in two (cytokinesis)
Pinching in two (cytokinesis)
splits, chromosomes uneven → Two cells with the wrong chromosomes
splits in two → Two healthy cells
splits, passing the mutation on → Two cells carrying a mutation

What TLC found

  • Holds: a cell never divides before it copies its DNA, and a cell never gets stuck.
  • Breaks without p53: damaged DNA gets copied, and both daughters carry the mutation (a path of 11 steps).
  • Breaks without the spindle check: the sisters are pulled apart too soon, and the daughters get the wrong chromosomes (a path of 9 steps).